executive
These are part of the executive branch.
judicial
State supreme courts (or their equivalent) are part of each State's Judicial branch.
A lieutenant governor is part of the executive branch in an individual state government. This is not a federal level elected official. In many states the lieutenant governors can run separately from the governor.
The Governor is the head of the Executive Branch of State Government, and in the same way the Prisident is head of the Executive Branch of the National Government.
(in the US) If you are referring to the Governor of a state - no, they cannot. The Governor is part of the Executive Branch of government not the Judicial Branch, therefore they cannot issue legal rulings.
He was order to take over important government buildings that belong to the German state government in Munich.
Wade Hampton III
Inherent
The Idaho Supreme Court is part of the Idaho Judicial branch because it's a state court.
because the Governor General represents the queen.
Jan Brewer is governor of the state of Arizona. The other three are all paid by the US federal government.